How to create a torus with divided cuts that correspond to the direction of the torus
Create the basic shape you want for your rings.



Add an array modifier to it.



Add a curve>Circle to the scene.

On you object add a curve modifier after the array and select the circle as object.



Depending select the correct axis for the curve modifier so that your array becomes an indented tours-like object.
Then adjust the settings for the array and the sizing of the object and the circle to your needs.